This experimental thesis has been done in the framework of AEgIS (Antimatter Experiment: Gravity, Interferometry, Spectroscopy), an experiment installed at CERN, whose primary goal is the measurement of the Earth's gravitational acceleration on anti-hydrogen. The antiatoms will be produced by the charge exchange reaction, where a cloud of Ps in Rydberg states interacts with cooled trapped antiprotons. Since the charge exchange cross section depends on Ps velocity and quantum number, the velocity distribution of Ps emitted by a positron-positronium converter as well as its excitation in Rydberg states have to be studied and optimized. In this thesis Ps cooling and emission into vacuum from nanochannelled silicon targets was studied by performing Time of Flight measurements with a dedicated apparatus conceived to receive the slow positron beam as produced at the Trento laboratory or at the NEPOMUC facility at Munich. Measurements were done by varying the positron implantation energy, the sample temperature and the nanochannel dimensions, with the aim of finding the best parameters to increase Ps fraction having velocity lower than 5 10^4 m/s. Preliminary data were analyzed in order to extract the Ps velocity distribution and its average temperature. More, an original method for evaluating the permanence time of Ps inside the nanochannels before being emitted into vacuum, was described. A first rough evaluation based on the performed measurements is reported and this result will be useful to investigate the Ps cooling process and to synchronize the laser pulse for Ps excitation in the AEgIS experiment. In order to perform measurements of Ps excitation in Rydberg states, a new apparatus for bunching positron pulses, coming from the AEgIS positron line, was designed and built. COMSOL and SIMION softwares were used for designing a magnetic transport line and an electron optical line, which extracts positrons from the magnetic field and focus them on the nanochanneled Si sample. More, a buncher device, which spatio-temporally compresses the positron bunches, was built and a fast circuit for supplying the 25 buncher electrodes with a parabolic shaped potential was designed and tested. According to the simulations, at the target position the device will deliver positrons with an energy ranging from 6 to 9 keV, in bunches of 5 ns duration and a spot of 2.5 mm in diameter. By using this apparatus, first measurements for the optimization of Ps excitation in Rydberg states and studies on the Ps levels with and without magnetic field will be performed. At a later stage investigations of Ps spectroscopy or of Ps laser cooling with the same apparatus could be achievable for the first time.

In this work we develop Quantum Monte Carlo techniques suitable for exploring both ground state and dynamical properties of interacting many-body systems. We then apply these techniques to the study of excitations in superfluid He4 and to explore the structure of nuclear systems using chiral effective field theory interactions.

In this work we discuss the role of topological degrees of freedom in very low-energy hadronic processes (vacuum polarization and vacuum birefringence). We also present an approach which enables to investigate the microscopic dynamics of non-perturbative processes: this is achieved by constructing an effective statistical theory for topological vacuum gauge configurations, by means of Lattice QCD simulations.

The thesis is devoted to my Ph.D. research activities during last three years within the CMS collaboration. My primary field of interest was the investigation of the Higgs sector of the Standard Model and in connection with Beyond-Standard-Model New Physics searches.

We analyze ground state properties of few-nucleons systems and $^{16}$O using \eftnopi (Pionless Effective Field Theory) at \ac{LO}. This is the first time the theory is extended to many-body nuclear systems. The free constants of the interaction are fitted using both experimental data and \ac{LQCD} results. The nuclear many-body Schr\"odinger equation is solved by means of the Auxiliary Field Diffusion Monte Carlo method. A linear optimization procedure has been used to recover the correct structure of the ground state wavefunction. {\eftnopi} as revealed to be an appropriate theory to describe light nuclei both in nature, and in the case where heavier quarks are used in order to make \ac{LQCD} calculation feasible. Our results are in good agreement with experiments and \ac{LQCD} predictions. In our \ac{LO} calculation, $^{16}$O appears to be unstable against breakup into four $^4$He for the quark masses considered.

Nuclei are objects made of nucleons, protons and neutrons. Several dynamical processes that occur in nuclei are of great interest for the scientific community and for possible applications. For example, nuclear fusion can help us produce a large amount of energy with a limited use of resources and environmental impact. Few-nucleon scattering is an essential ingredient to understand and describe the physics of the core of a star. The classical computational algorithms that aim to simulate microscopic quantum systems suffer from the exponential growth of the computational time when the number of particles is increased. Even using today's most powerful HPC devices, the simulation of many processes, such as the nuclear scattering and fusion, is out of reach due to the excessive amount of computational time needed. In the 1980s, Feynman suggested that quantum computers might be more efficient than classical devices in simulating many-particle quantum systems. Following Feynman's idea of quantum computing, a complete change in the computation devices and in the simulation protocols has been explored in the recent years, moving towards quantum computations. Recently, the perspective of a realistic implementation of efficient quantum calculations was proved both experimentally and theoretically. Nevertheless, we are not in an era of fully functional quantum devices yet, but rather in the so-called "Noisy Intermediate-Scale Quantum" (NISQ) era. As of today, quantum simulations still suffer from the limitations of imperfect gate implementations and the quantum noise of the machine that impair the performance of the device. In this NISQ era, studies of complex nuclear systems are out of reach. The evolution and improvement of quantum devices will hopefully help us solve hard quantum problems in the coming years. At present quantum machines can be used to produce demonstrations or, at best, preliminary studies of the dynamics of a few nucleons systems (or other equivalent simple quantum systems). These systems are to be considered mostly toy models for developing prospective quantum algorithms. However, in the future, these algorithms may become efficient enough to allow simulating complex quantum systems in a quantum device, proving more efficient than classical devices, and eventually helping us study hard quantum systems. This is the main goal of this work, developing quantum algorithms, potentially useful in studying the quantum many body problem, and attempting to implement such quantum algorithms in different, existing quantum devices. In particular, the simulations made use of the IBM QPU's , of the Advanced Quantum Testbed (AQT) at Lawrence Berkeley National Laboratory (LBNL), and of the quantum testbed recently based at Lawrence Livermore National Laboratory (LLNL) (or using a device-level simulator of this machine). The our research aims are to develop quantum algorithms for general quantum processors. Therefore, the same developed quantum algorithms are implemented in different quantum processors to test their efficiency. Moreover, some uses of quantum processors are also conditioned by their availability during the time span of my PhD. The most common way to implement some quantum algorithms is to combine a discrete set of so-called elementary gates. A quantum operation is then realized in term of a sequence of such gates. This approach suffers from the large number of gates (depth of a quantum circuit) generally needed to describe the dynamics of a complex system. An excessively large circuit depth is problematic, since the presence of quantum noise would effectively erase all the information during the simulation. It is still possible to use error-correction techniques, but they require a huge amount of extra quantum register (ancilla qubits). An alternative technique that can be used to address these problems is the so-called "optimal control technique". Specifically, rather than employing a set of pre-packaged quantum gates, it is possible to optimize the external physical drive (for example, a suitably modulated electromagnetic pulse) that encodes a multi-level complex quantum gate. In this thesis, we start from the work of Holland et al. "Optimal control for the quantum simulation of nuclear dynamics" Physical Review A 101.6 (2020): 062307, where a quantum simulation of real-time neutron-neutron dynamics is proposed, in which the propagation of the system is enacted by a single dense multi-level gate derived from the nuclear spin-interaction at leading order (LO) of chiral effective field theory (EFT) through an optimal control technique. Hence, we will generalize the two neutron spin simulations, re-including spatial degrees of freedom with a hybrid algorithm. The spin dynamics are implemented within the quantum processor and the spatial dynamics are computed applying classical algorithms. We called this method classical-quantum coprocessing. The quantum simulations using optimized optimal control methods and discrete get set approach will be presented. By applying the coprocessing scheme through the optimal control, we have a possible bottleneck due to the requested classical computational time to compute the microwave pulses. A solution to this problem will be presented. Furthermore, an investigation of an improved way to efficiently compile quantum circuits based on the Similarity Renormalization Group will be discussed. This method simplifies the compilation in terms of digital gates. The most important result contained in this thesis is the development of an algorithm for performing an imaginary time propagation on a quantum chip. It belongs to the class of methods for evaluating the ground state of a quantum system, based on operating a Wick rotation of the real time evolution operator. The resulting propagator is not unitary, implementing in some way a dissipation mechanism that naturally leads the system towards its lowest energy state. Evolution in imaginary time is a well-known technique for finding the ground state of quantum many-body systems. It is at the heart of several numerical methods, including Quantum Monte Carlo techniques, that have been used with great success in quantum chemistry, condensed matter and nuclear physics. The classical implementations of imaginary time propagation suffer (with few exceptions) of an exponential increase in the computational cost with the dimension of the system. This fact calls for a generalization of the algorithm to quantum computers. The proposed algorithm is implemented by expanding the Hilbert space of the system under investigation by means of ancillary qubits. The projection is obtained by applying a series of unitary transformations having the effect of dissipating the components of the initial state along excited states of the Hamiltonian into the ancillary space. A measurement of the ancillary qubit(s) will then remove such components, effectively implementing a "cooling" of the system. The theory and testing of this method, along with some proposals for improvements will be thoroughly discussed in the dedicated chapter.

The work presents the recent developments in Quantum Monte Carlo calculations for nuclear systems including strange degrees of freedom. The Auxiliary Field Diffusion Monte Carlo algorithm has been extended to the strange sector by the inclusion of the lightest among the hyperons, the Λ particle. This allows to perform detailed calculations for Λ hypernuclei, providing a microscopic framework for the study of the hyperon-nucleon interaction in connection with the available experimental information. The extension of the method for strange neutron matter, put the basis for the first Diffusion Monte Carlo analysis of the hypernuclear medium, with the derivation of neutron star observables of great astrophysical interest.

Introduction In this thesis I report the work of my PhD; it treated two different topics, both related by a third one, that is the computational method that I use to solve them. I worked on EFT-theories for nuclear systems and on Hypernuclei. I tried to compute the ground state properties of both systems using Monte Carlo methods. In the first part of my thesis I briefly describe the Monte Carlo methods that I used: VMC (Variational Monte Carlo), DMC (Diffusion Monte Carlo), AFDMC (Auxiliary Field Diffusion Monte Carlo) and AFQMC (Auxiliary Field Quantum Monte Carlo) algorithms. I also report some new improvements relative to these methods that I tried or suggested: I remember the fixed hypernode extension (§ 2.6.2) for the DMC algorithm, the inclusion of the L2 term (§ 3.10) and of the exchange term (§ 3.11) into the AFDMC propagator. These last two are based on the same idea used by K. Schmidt to include the spin-orbit term in the AFDMC propagator (§ 3.9). We mainly use the AFDMC algorithm but at the end of the first part I describe also the AFQMC method. This is quite similar in principle to AFDMC, but it was newer used for nuclear systems. Moreover, there are some details that let us hope to be able to overcome with AFQMC some limitations that we find in AFDMC algorithm. However we do not report any result relative to AFQMC algorithm, because we start to implement it in the last months and our code still requires many tests and debug. In the second part I report our attempt of describing the nucleon-nucleon interaction using EFT-theory within AFDMC method. I explain all our tests to solve the ground state of a nucleus within this method; hence I show also the problems that we found and the attempts that we tried to overcome them before to leave this project. In the third part I report our work about Hypernuclei; we tried to fit part of the ΛN interaction and to compute the Hypernuclei Λ-hyperon separation energy. Nevertheless we found some good and encouraging results, we noticed that the fixed-phase approximation used in AFDMC algorithm was not so small like assumed. Because of that, in order to obtain interesting results, we need to improve this approximations or to use a better method; hence we looked at AFQMC algorithm aiming to quickly reach good results.

The Bethe-Weizsäcker cycle consists of a set of nuclear reactions that convert hydrogen into helium and release energy in the stars. It determines the luminosity of low-metal stars at their turn-off from the main-sequence in the Hertzsprung-Russel diagram, so its rate enters the calculation of the globular clusters’ age, an independent lower limit on the age of the universe. The cycle contributes less than 1% to our Sun’s luminosity, but it produces neutrinos that can in principle be measured on Earth in underground experiments and bring direct information of the physical conditions in the solar core, provided that the nuclear reaction rate is known with sufficient precision. The 14N(p,γ)15O reaction is the slowest reaction of the Bethe-Weizs¨acker cycle and establishes its rate. Its cross section is the sum of the contributions by capture to different excited levels and to the ground state in 15O. Recent experiments studied the region of the resonance at Ep = 278 keV. Only one modern data set from an experiment performed in 1987 is available for the high-energy domain. Both energy ranges are needed to constrain the fit of the excitation function in the R-matrix framework and to obtain a reliable extrapolated S-factor at the very low astrophysical energies. The present research work studied the 14N(p,γ)15O reaction in the LUNA (Laboratory for Underground Nuclear Astrophysics) underground facility at three proton energies 0.36, 0.38, 0.40MeV, and in Dresden in the energy range Ep = 0.6 - 2MeV. In both cases, an intense proton beam was sent on solid titanium nitride sputtered targets, and the prompt photons emitted from the reaction were detected with germanium detectors. At LUNA, a composite germanium detector was used. This enabled a measurement with dramatically reduced summing corrections with respect to previous studies. The cross sections for capture to the ground state and to the excited states at 5181, 6172, and 6792 keV in 15O have been determined. An R-matrix fit was performed for capture to the ground state, that resolved the literature discrepancy of a factor two on the extrapolated S-factor. New precise branching ratios for the decay of the Ep = 278 keV resonance were measured. In Dresden, the strength of the Ep = 1058 keV resonance was measured relative to the well-known resonance at Ep = 278 keV, after checking the angular distribution. Its uncertainty is now half of the error quoted in literature. The branching ratios were also measured, showing that their recommended values should be updated. Preliminary data for the two most intense transitions off resonance are provided. The presence in the targets of the other stable nitrogen isotope 15N with its well- known isotopic abundance, allowed to measure the strength of two resonances at Ep = 430 and 897 keV of the 15N(p,αγ)12 C reaction, improving the precision for hydrogen depth profiling.

The Bethe-Weizsäcker cycle consists of a set of nuclear reactions that convert hydrogen into helium and release energy in the stars. It determines the luminosity of low-metal stars at their turn-off from the main-sequence in the Hertzsprung-Russel diagram, so its rate enters the calculation of the globular clusters’ age, an independent lower limit on the age of the universe. The cycle contributes less than 1% to our Sun’s luminosity, but it produces neutrinos that can in principle be measured on Earth in underground experiments and bring direct information of the physical conditions in the solar core, provided that the nuclear reaction rate is known with sufficient precision. The 14N(p,γ)15O reaction is the slowest reaction of the Bethe-Weizs¨acker cycle and establishes its rate. Its cross section is the sum of the contributions by capture to different excited levels and to the ground state in 15O. Recent experiments studied the region of the resonance at Ep = 278 keV. Only one modern data set from an experiment performed in 1987 is available for the high-energy domain. Both energy ranges are needed to constrain the fit of the excitation function in the R-matrix framework and to obtain a reliable extrapolated S-factor at the very low astrophysical energies. The present research work studied the 14N(p,γ)15O reaction in the LUNA (Laboratory for Underground Nuclear Astrophysics) underground facility at three proton energies 0.36, 0.38, 0.40MeV, and in Dresden in the energy range Ep = 0.6 - 2MeV. In both cases, an intense proton beam was sent on solid titanium nitride sputtered targets, and the prompt photons emitted from the reaction were detected with germanium detectors. At LUNA, a composite germanium detector was used. This enabled a measurement with dramatically reduced summing corrections with respect to previous studies. The cross sections for capture to the ground state and to the excited states at 5181, 6172, and 6792 keV in 15O have been determined. An R-matrix fit was performed for capture to the ground state, that resolved the literature discrepancy of a factor two on the extrapolated S-factor. New precise branching ratios for the decay of the Ep = 278 keV resonance were measured. In Dresden, the strength of the Ep = 1058 keV resonance was measured relative to the well-known resonance at Ep = 278 keV, after checking the angular distribution. Its uncertainty is now half of the error quoted in literature. The branching ratios were also measured, showing that their recommended values should be updated. Preliminary data for the two most intense transitions off resonance are provided. The presence in the targets of the other stable nitrogen isotope 15N with its well- known isotopic abundance, allowed to measure the strength of two resonances at Ep = 430 and 897 keV of the 15N(p,αγ)12 C reaction, improving the precision for hydrogen depth profiling.